$\sqrt {[12 - \sqrt {(68 + 48\sqrt 2 )} ]} = $
Medium
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b
(b) \(\sqrt {12 - \sqrt {68 + 48\sqrt 2 } } = \sqrt {12 - \sqrt {{6^2} + {{(4\sqrt 2 )}^2} + 2.6.4\sqrt 2 } } \)
(b) \(\sqrt {12 - \sqrt {68 + 48\sqrt 2 } } = \sqrt {12 - \sqrt {{6^2} + {{(4\sqrt 2 )}^2} + 2.6.4\sqrt 2 } } \)
\(= \sqrt {12 - \sqrt {{{(6 + 4\sqrt 2 )}^2}} } \)= \(\sqrt {12 - 6 - 4\sqrt 2 } = \sqrt {6 - 4\sqrt 2 } \)
\(= \sqrt {{2^2} + {{(\sqrt 2 )}^2} - 2\,.\,2\sqrt 2 } = 2 - \sqrt 2 \).
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